Constructing the fractional series solutions for time-fractional K-dV equation using Laplace residual power series technique

In this article, we construct the series solution of the time-fractional Korteveg de Vries (K-dV) equation through a computational approach named as Laplace residual power series (LRPS) that combines the Laplace transform with the residual power series method (RPS). Time-fractional K-dV equation is used to modeled various real life phenomena like propagation of waves in elastic rods, dispersion effects in shallow coastal regions, anomalous diffusion observed in financial markets. The Caputo fractional derivative is used in the formulation of time-fractional K-dV equation. LRPS method is characterized by its rapid convergence and easy finding of the unknown coefficients using the concept of limit at infinity without any perturbation, discretization and linearization. To assess the effectiveness of proposed computational strategy, we perform a comparative analysis among the fractional residual power series method, the Adomian decomposition method, and the RPS method. Additionally, we examine the convergence of the fractional series solution across different α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} values and assess the solution’s behavior as the time domain increased. The efficiency and authenticity of the LRPS method is shown by computing the absolute error, relative error and residual error. This work is supported by 2D and 3D graphical representations made in accordance with Maple and MATLAB.